3 ms·
I had a similar eyeroll but I was wrong. It's not a polyhedron. Polygedrons have planar faces. The scutoids here have curved faces on one of "pentagonal" the
by kjeetgill 8y ago
I had a similar eyeroll but I was wrong.
It's not a polyhedron.
Polygedrons have planar faces. The scutoids here have curved faces on one of "pentagonal" the "walls". The 5 points for that wall aren't nessecarily coplanar.
An interesting property of that face is that it compliments another scutoid. See either YouTube link elsewhere.
From Wikipedia:
Scutoids are not necessarily convex, and lateral faces are not necessarily planar, so several scutoids can pack together to fill all the space between the two parallel surfaces.
- romwell 8y agoSure, make it "up to diffeomorphism". The shapes you get fit in a larger class of piecewise-smooth closed surfaces, but all the interesting information is encoded in the polyhedron. Note that the other shapes they're dealing with - e.g. prisms - also don't have planar faces (but are defined as having such on Wikipedia). The point is that mathematical definitions are quite malleable, and depend on the context. "Lop a vertex off a prism and deform a bit" is hardly a radical notion in itself. As for combining these shapes - the term for that is tiling or tessellation. You can tesselate the space with all kinds of shapes. The "faces match" is a property of objects a tessellation, not of any given object in itself.